The fundamental conceptual difficulty in mark-to-future is the ability
to generate scenarios that mimic reality. The challenge, even in the
static case, is to capture multidimensional distributions with very
limited amount of historical information.

In this paper, we overview existing as well as new methodologies in the
generic area of scenarion generation, and introduce a collection of
benchmarks to evaluate the accuracy of each technique. Finally, we
apply our methodology to a number of business cases.

Since the pioneering work of Mandelbrot and Fama in the early 1960s,
evidence has accumulated that many financial indices follow Levy (or
stable) distributions, which arise naturally as the limiting
distributions of large aggregations of variates with Pareto (or power
law) distributions. Recent research on self-organizing criticality (a
proposed generator for Pareto laws) has rekindled interest on the
ubiquity of Pareto laws in financial data.

Although the problem of estimating univariate Levy distributions has
been well-studied, little is known about estimating multivariate
distributions. Unlike the Gaussian case, the multivariate Levy case is
not a simple generalization of the univariate case. Multivariate Levy
distributions exhibit a rich and subtle dependence structure, which,
strongly influences the distribution of extreme events. Accurately
estimating this dependence structure (and understanding its
consequences) is therefore critical for multifactor risk management in
a Levy regime.

We have developed methods to estimate multivariate Levy distributions
from empirical data. Once the distribution is known, methods of
multifactor portfolio optimization can be used to manage risk. This
methodology is used to produce software to simulate multivariate Levy
data; a known distribution can be used to generate synthetic scenarios
with which to stress-test risk-management strategies. They would also
provide a framework for mark-to-future analysis.

Energy markets and specially electricity markets are a lot more complex
than equity or interest rate or foreign exchange markets. I will
discuss some issues regarding the modeling of the underlying price
processes, their applications to some exotic energy derivatives and
their numerical implementations.

I will describe some joint work with Moshe Milevsky and Scott Warlow,
concerning the pricing of stock baskets. These baskets have knockout
provisions, so that stocks may be thrown out of the basket depending on
their performance relative to other components of the basket. The
mathematical tools involved include conditioned Brownian motion. The
financial motivation is the quantification of survivorship bias.